Problem Description
An integer n is strictly palindromic if, for every base b between 2 and n - 2 (inclusive), the string representation of the integer n in base b is palindromic. Given an integer n, return true if n is strictly palindromic and false otherwise. A string is palindromic if it reads the same forward and backward.
Key Insights
- A strictly palindromic number must be palindromic in all bases from 2 to n - 2.
- For any n >= 4, you can find that n is not strictly palindromic since, in base n-1, n would be represented as "11", which is always palindromic.
- However, in base 2, the representation of n will generally not be palindromic for n >= 4.
- Thus, no integer n >= 4 can be strictly palindromic.
Space and Time Complexity
Time Complexity: O(1)
Space Complexity: O(1)
Solution
The solution involves understanding the properties of number bases and palindromes. Since a strictly palindromic number must be palindromic in all bases from 2 to n - 2, and we can quickly determine that for any n >= 4, it cannot satisfy the palindromic condition in at least one base (e.g., base 2), we can conclude that the answer is always false for n >= 4.